Hsiao, George C.2004-12-222004-12-222004http://udspace.udel.edu/handle/19716/209Dedicated to Professor Dr. Wolfgang L.Wendland in Friendship and Admiration. This paper is based on a plenary lecture entitled Boundary Element Methods – past, present and the future, delivered by the author at the First Chilean Workshop on Numerical Analysis of Partial Differential Equations, Universidal de Concepcion, Chile, January 13-16, 2004.Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. This paper gives an overview of the method from both theoretical and numerical point of view. It summaries the main results obtained by the author and his collaborators over the last 30 years. Fundamental theory and various applications will be illustrated through simple examples. Some numerical experiments in elasticity as well as in fluid mechanics will be included to demonstrate the efficiency of the methods.1249288 bytesapplication/pdfen-USBoundary integral equationsfundamental solutionsvariational formulationsSobolev spacesweak solutionsGarding’s inequalityGalerkin’s methodboundary elementsstabilityill-posednessasymptotic error estimatesAMS: 35J20, 45B05, 65N30Technical Report